I had this exact problem for years (dual use hifi and home theatre) and it can be overcome without room treatment or tv covers.
Proper speaker positioning. I use Ron’s LOTS method - he has a video on YouTube. Once dialed in the difference between an open and holographic soundstage and something bland was as little as 1cm in positioning.
Funny thing, I once got my speakers setup perfectly, then 6 months later upgraded the tv from a 55” curved to a 65” flat panel. This single change was enough to destroy all that work and the glorious soundstage I had.
But it shows how critical the speaker positioning was to overcoming the centre reflection issue.
I also had a tv cover custom sown and tried it after optimising with the LOTS method. It actually made things worse, because the positioning had already been done to account for the tv reflection. That’s also why changing to a different tv size had such an effect.